The application of the boundary-integral equation method to the solution of engineering stress analysis and fracture mechanics problems

This paper reviews the development and application of an influence function method for calculating stress intensity factors and residual fatigue life for two- and three-dimensional structures with complex stress fields and geometries. Through elastic superposition the method properly accounts for redistribution of stress as the crack grows through the structure. The analytical methods utilized and the computer programs necessary for computation and application of load independent influence functions are presented. A new exact solution is obtained for the buried elliptical crack, under an arbitrary Mode I stress field, for stress intensity factors at four positions around the crack front. The IF method is then applied to two fracture mechanics problems with complex stress fields and geometries. These problems are of current interest to the electric power generating industry and include (1) the fatigue analysis of a crack in a pipe weld under nomial and residual stresses and (2) fatigue analysis of a reactor pressure vessel nozzle corner crack under a complex bivariate stress field.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

An elastic–plastic fracture mechanics based methodology to characterize cracking behavior and its application to environmental assisted processes

Cracking processes suffered by new structural and piping steels when used in petroleum or other energy installations have demonstrated the need for a cracking resistance characterization methodology. This methodology, valid for both elastic and elastoplastic regimes, should be able to define crack propagation kinetics as a function of their controlling local parameters. This work summarizes an experimental and analytical methodology that has been shown to be suitable for characterizing cracking processes using compact tensile specimens, especially subcritical environmentally assisted ones, such as those induced by hydrogen in microalloyed steels. The applied and validated methodology has been shown to offer quantitative results of cracking behavior and to correlate these with the existing fracture micromechanisms.     

An engineering fracture mechanics analysis of the Pilgrim I nozzle-to-pressure vessel weld discontinuities

The influence function method for calculation of stress intensity factor K_I(a) is applied to the case of a semicircular surface crack, of radius a, used to model a discontinuity revealed by in-service inspection of a nozzle-to-shell weld in the Pilgrim I pressure vessel. Results of the analysis are discussed in detail.     

Applications of probabilistic fracture mechanics to FBR components

A probabilistic fracture mechanics code which evaluates fracture probability of a plate model with an elliptical surface crack caused by creep-fatigue crack growth has been developed. The code named PCCF (Probabilistic Fracture Mechanics Code for Creep-Fatigue Crack Growth) uses simplified methods of C^* and J-integral for evaluation of creep-fatigue crack growth and a stratified sampling method for two input variables to improve the solution convergency. According to the test analyses focused on an applied stress level using PCCF code, leak probability is sensitive to a stress level and increases rapidly when an applied stress is close to a yield stress level.     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson-Tvergaard-Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness (J_SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J_SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.     

The use of fracture mechanics and non-destructive testing to reduce the risk of catastrophic failure

Structural integrity assessments involve the use of fracture mechanics together with appropriate design, quality assurance and inspection techniques. Recent application to nuclear pressure vessels has led to improvements in the fracture toughness data base, in methods for measuring fracture toughness and in the use of elastic/plastic and J?R curve concepts. Fatigue crack growth studies in water of realistic flow rate and oxygen content have shown that the effect of a PWR water environment is not as severe as previously reported and has related this to show strain rate cracking. The role of the pressure test has beenn examined, throwing emphasis on the importance of effective non-destructive inspection to detect and characterise flaws. Recent developments to improve and to validate very high levels of effectiveness of NDT are summarised.     

Application of fracture mechanics concepts to the failure of wide plates

An analysis is presented to predict the failure behaviour of wide plates with different crack lengths in a temperature range where brittle, elastic-plastic and fully ductile behaviour is observed. Comparing the characteristic material properties derived from small scale specimens with the corresponding loading conditions in terms of J_appl using two- and three-dimensional finite element analyses, the failure loads can be calculated as a function of temperature. Based on these analyses it is possible to predict the different failure behaviour of the wide plates characterized by the transition temperatures T_gy and T_i.     

Degradation of fracture mechanics properties of reactor graphite due to burn-off

This paper evaluates the change in various mechanical and fracture mechanics properties of two kinds of graphite for high temperature gas-cooled reactors due to burn-off by air oxidation. Thermal shock resistance and thermal shock fracture toughness of the burn-off graphite are also quantitatively determined by using an arc discharge heating method. These results are expressed as a function of burn-off, B, by an empirical formula of the form; S = S₀exp(−nB), where S₀ and n denote respectively the initial value and the degradation exponent of the material. The empirical formulas for thermal shock are found to agree reasonably well with those calculated from the results of individually examining the effect of burn-off on the associated properties.     

Application and evaluation of fracture mechanics failure concepts to precracked vessels

The elastic-plastic fracture mechanics concepts R-curve method, Two Criteria Approach, COD concept and Battelle formula were applied on three tested vessels made of low and high tough and fine grained structural steel and X 8 Ni 9 with an axial notch on the outer surface. Apart from the R-curve method for the vessel made of low tough material, failure loads were conservatively calculated. The COD concept could not be applied to these vessels and failure geometries using the well known design curve. A modification of the COD concept by means of FE-calculations was made so that a correlation between the displacement at the crack tip and at the vessel surface could be determined. With this procedure, the calculated load at fracture was only 8% below the experimental result.     

Some recently-developed analytical aspects of fracture mechanics

The paper aims to describe new approaches to fracture mechanics which take into account local damage of the material, with special reference to materials susceptible to sudden damage. The basic idea is that classical stress-strain laws are valid only below a given deformation threshold, _R. Above that threshold, the stresses irreversibly fall towards zero. The classical crack concept is then replaced by that of a quasi-crack with a process or damaged zone of finite, non-zero thickness. On the basis of the energy equation and drawing a distinction between the plastic work and fracture rates, it is demonstrated how the R curve can be obtained. The cases of brittle and ductile fracture are discussed. In order to rejoin the classical theories of fracture mechanics, it is sufficient to extend the deformation threshold _R towards infinity. The ratio between fracture energy and energy dissipated through plastic work tends towards zero at that limit. In the damage fracture theory presented here, where _R is finite, the fracture energy is other than zero.     

Risk–benefit analyses of SG tube maintenance based on probabilistic fracture mechanics

As an application of probabilistic fracture mechanics (PFM), a risk–benefit analysis was performed for the purpose of optimizing maintenance activities of steam generator (SG) tubes used in pressurized water reactors (PWRs). The probabilities of the SG tube leakage and rupture are defined as risks in this study. A model was made modifying pc-PRAISE (Piping Reliability Analysis Including Seismic Events) to evaluate the risks during 60 year operations due to stress corrosion cracking (SCC) of the tubes under various maintenance strategies for SG tubes.In the risk analysis, parameters such as inspection accuracy, inspection interval, sampling inspection and crack propagation law were selected for sensitivity analysis. Based on the risk analysis, a risk–benefit analysis was conducted when implementing two maintenance strategies taking both costs and revenues for 60 year operations into account. In the risk–benefit analysis, the expected cost of leakage or rupture was calculated by multiplying ‘probability of leakage or rupture’ by ‘expected loss of leakage or rupture accident’. To justify whether it is worthwhile implementing the maintenance strategies or not, the net present value (NPV) was calculated as an index, which is one of the most fundamental financial indices for decision-making based on the discounted cash flow (DCF) method.The results demonstrated that in the risk analysis, the risks are influenced significantly by the crack propagation law, accuracy of inspection and sampling inspection. In the risk–benefit analysis, it was suggested that investment to improve inspection accuracy would reduce the total costs of 60 year operations significantly and increase the NPV.Although the analysis was mainly conducted for SG tubes made of Inconel 600 mill anneal (MA) material, the analysis was also carried out for Inconel 690 thermal treatment (TT) material, making assumptions on its crack initiation and crack propagation law. In addition, the effect of introducing maintenance criteria, namely, operation with a crack justified by certain criteria, on NPV was evaluated.     

Application of statistical linear elastic fracture mechanics to pressure vessel reliability analysis

An evaluation of the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length. The probability of failure is the joint probability that there exists a crack (i.e. K_I) greater than a given crack (i.e. K) and that the critical crack (i.e. K_IC) is smaller than that same crack, where K_I and K_IC are considered for same time and location. K_IC as well as K_I are treated as statistical variables with probability density functions (p.d.f.), which are functions of material, location and time. The variability of K_IC (that is the p.d.f. of K_IC) is a result primarily of the statistical nature of the material properties and to a lesser degree of the increasing neutron-done experienced by certain parts of the pressure vessel. The variability of K_I (that is the p.d.f. of K_I) is a result of the following parameters:

1. (1) initial distribution of cracks (that is the crack distribution at the start-up of the reactor) regarded as a statistical variable, because of the uncertainty in the non-destructive testing of the pressure vessel prior to start-up.

2. (2) stresses, regarded as a statistical variable because of the uncertainty in the stress analysis and the geometry of the vessel.

3. (3) crack growth by fatigue, which is a result of the normal (with probability equal to 1.0) and abnormal (with a p.d.f.) operational transients. The statistical nature of the crack growth is due to the statistical variation of the abnormal operational transients.

4. (4) material properties (that is K_IC, yield strength and the factors governing the fatigue crack growth) regarded as statistical variables.

The p.d.f.s of the abovementioned parameters are evaluated on the basis of the available literature. The integrated calculations of failure probability are performed by a computer program utilizing the Monte Carlo technique with importance sampling, which gives a greater freedom in selection of p.d.f.s. Calculations of failure probability for existing reactors are presented.     

Reference stress based fracture mechanics analysis for circumferential through-wall cracked pipes: experimental validation

This paper presents experimental validation of the reference stress based J estimates for circumferential through-wall cracked (TWC) pipes, recently proposed by the authors. Using the pipe test data for circumferential TWC pipes given in the Pipe Fracture Encyclopedia [Pipe Fracture Test Data, vol. 3, Battelle, 1997], the predicted fracture initiation and instability loads according to the proposed reference stress method are compared with experimental ones as well as predictions according to the reference stress method embedded in R6. The results show that both the R6 method and the proposed method give conservative estimates of initiation and maximum moments for circumferential TWC pipes, compared to experimental data. For longer cracks, the proposed method reduces the conservatism embedded in the estimated J according to the R6 method, and the resulting predictions are less conservative, compared to those from the R6 method. For shorter cracks, on the other hand, the proposed method reduces possible non-conservatism embedded in estimated J according to the R6 method, and the resulting predictions are slightly more conservative.     

A statistical based circumferentially cracked pipe fracture mechanics analysis for design or code implementation

This paper discusses a simple engineering approach to evaluate surface flaws in carbon steel or stainless steel piping and their weldments. It is based on statistical data from a large number of pipe fracture experiments. To ensure a reasonably conservative approach, a 95-percent confidence level was established. Toughness and pipe size effects are accounted for in one correction factor, while ovalization and flow stress effects are accounted for in two other factors. The limitations and possible improvements to such an approach are also discussed.     

An elasto-plastic fracture mechanics based model for assessment of hydride embrittlement in zircaloy cladding tubes

This paper describes a finite element based fracture mechanics model to assess how hydrides affect the integrity of zircaloy cladding tubes. The hydrides are assumed to fracture at a low load whereas the propagation of the fractured hydrides in the matrix material and failure of the tube is controlled by non-linear fracture mechanics and plastic collapse of the ligaments between the hydrides. The paper quantifies the relative importance of hydride geometrical parameters such as size, orientation and location of individual hydrides and interaction between adjacent hydrides. The paper also presents analyses for some different and representative multi-hydride configurations. The model is adaptable to general and complex crack configurations and can therefore be used to assess realistic hydride configurations. The mechanism of cladding failure is by plastic collapse of ligaments between interacting fractured hydrides. The results show that the integrity can be drastically reduced when several radial hydrides form continuous patterns.     

Integration of nondestructive examination reliability and fracture mechanics

A multi-year program at the Pacific Northwest Laboratory is in progress to determine the reliability of ultrasonic ISI that is performed on light-water reactor primary systems, using probabilistic fracture mechanics (FM) analysis to determine the impact of NDE unreliability on system safety, and to evaluate advanced ultrasonic techniques. This paper is a review of the last year's highlights. Emphasis is placed upon the results of a pipe inspection round robin, advanced technique evaluation, joint study with Westinghouse, qualification document, underclad crack detection sizing studies, and a FM analysis using the PRAISE code for studying inspection parameters.     

Integration of nondestructive examination reliability and fracture mechanics

A multi-year program on the Integration of Nondestructive Examination and Fracture Mechanics (NDE/FM) has been funded by the U.S. Nuclear Regulatory Commission at the Pacific Northwest Laboratory. Many activities are being pursued under this program. This paper highlights some of the activities: input to the NRC Pipe Crack Task Group, an evaluation of manual ultrasonic testing of centrifugally cast stainless steel, interaction matrix, advanced UT technique evaluation, qualification document, evaluation of crack characterization techniques, international NDE reliability work, siamese imaging technique for imaging planar-type radial defects in reactor piping, fracture mechanics analysis for PTS-type flaws and piping reliability, and a position paper on piping ISI.